Motion of Quantized Vortices as Elementary Objects

TL;DR

This paper derives the fundamental equations governing the motion of quantized vortices in superfluids using a relativistic, coordinate-invariant framework, emphasizing topological stability and hydrodynamic collective coordinates.

Contribution

It introduces a novel derivation of vortex motion equations from a relativistic, invariant formalism, considering vortex interactions and quantization in superfluid hydrodynamics.

Findings

Derived vortex equations of motion from a relativistic framework

Separated Magnus force and vortex self-interaction effects

Quantized vortex motion using collective coordinates

Abstract

The general local, nondissipative equations of motion for a quantized vortex moving in an uncharged laboratory superfluid are derived from a relativistic, co-ordinate invariant framework, having vortices as its elementary objects in the form of stable topological excitations. This derivation is carried out for a pure superfluid with isotropic gap at the absolute zero of temperature, on the level of a hydrodynamic, collective co-ordinate description. In the formalism, we use as fundamental ingredients that particle number as well as vorticity are conserved, and that the fluid is perfect. No assumptions are involved as regards the dynamical behaviour of the order parameter. The interaction of the vortex with the background fluid, representing the Magnus force, and with itself via phonons, giving rise to the hydrodynamic vortex mass, are separated. For a description of the motion of the vortex in a dense laboratory superfluid like helium II, two limits have to be considered: The nonrelativistic limit for the superfluid background is taken, and the motion of the vortex is restricted to velocities much less than the speed of sound. The canonical structure of vortex motion in terms of the collective co-ordinate is used for the quantization of this motion.